Chemistry 324 - Spring 2008

I have posted some background information on energy calculations here (required reading).

I have also repeated the calculations that you performed in class and posted the results below. The comparison of reactions, and the comparison of different methods for calculating reaction enthalpies, are very interesting. But let’s start with the raw data first.

AM1 Reaction enthalpies (298 K)

1. Number under molecule is its AM1 heat of formation (kcal/mol)

2. Number on right (bold) is the AM1 reaction enthalpy (kcal/mol). Some of my numbers (which I trust completely) are different from what you reported. Since I don’t have your heats of formation, I can’t account for any discrepancies.

3. Consistent with your predictions, the addition of CO2 is not nearly as favorable as the addition of ethylene. However, the additions of CO2 and MeCN are both predicted to be exothermic.

Hartree-Fock/3-21G Reaction enthalpies (0 K)

1. Number on right is the HF/3-21G reaction enthalpy at 0 K (kcal/mol). This combines the total energy and the zero-point energy (ZPE), but does not include PV work (< 1 kcal/mol) or the effects of warming from 0 K to 298 K (typically < 1 kcal/mol).

2. The HF/3-21G enthalpies are very different from the AM1 enthalpies. In fact, the differences are so large, they cannot be due to the different temperatures that were assumed. The two tools give similar qualitative results for ethylene vs. CO2 vs. MeCN, but the quantitative agreement is poor.

Better Energies

Mark Twain once said that a man with two watches never knew what time it was. The same can be said about someone who has used two tools for calculating energies. Which answer is right? Is either answer right?

One way to answer these questions is to change tools and re-calculate the energies. Since other tools will use different approximations, we might learn whether AM1 or HF/3-21G was more reliable. An even better approach is to use a tool that uses fewer approximations. The following table shows two sets of reaction enthalpies (0 K) obtained using a post-Hartree-Fock tool (MP2) and a density functional theory-based tool (B3LYP).

The results are quite surprising.

1. The energies obtained with the higher-level tools agree with each other for two reactions, but not the third (the simple Diels-Alder). The addition of CO2 is predicted to be endothermic and the reaction enthalpies for CO2 and MeCN are very different from each other.

2. The energies obtained with the higher-level tools do not agree with the lower-level energies. Neither AM1 nor HF/3-21G is quantitatively reliable. This is especially the case when the types of chemical bonds in the reactants and products are different (the next section shows a case where AM1 and HF/3-21G do much better).

3. Even qualitative predictions can be risky. The low-level tools predicted 3 exothermic reactions. Wrong! The low-level tools predicted fairly similar behavior for CO2 and MeCN (reaction enthalpies differ by < 10 kcal/mol). Wrong! The low-level tools were correct, however, in predicting a very exothermic Diels-Alder reaction for ethylene.

Endo v. Exo (Isomer energies)

The previous section shows that reaction enthalpies are hard to calculate reliably when the starting materials and products contain different kinds of bonds.

Reliable energies can be obtained, however, when the same kinds of bonds appear on both sides of the reaction arrow, as in the following epimerization:

The energy of the endo isomer relative to the exo isomer (obtained using the same 4 tools described above) is listed below:

All of the calculated energies fall within a 1.5 kcal/mol range showing that low-level and high-level tools can give consistent results for certain systems. Unfortunately, the range energies includes zero, so one tool (MP2) predicts the endo isomer as more stable while the others predict the exo isomer as more stable.

When calculated energy differences are as small as these, one should include all relevant energy corrections (ZPE, warming to 298 K, and so on). I haven’t done this. The three ab initio energies are relative “total” energies only.

Round off your energy (at the end of the calculation)

Computers calculate very precisely and produce results with lots of figures after the decimal point. The accuracy of these calculations tends to be abysmal, however, so there is no need to get carried away and include lots of figures in the final energies. If you look at my tables and figures, you will see that I generally round reaction enthalpies (but not molecular energies) to +/- 0.1 kcal/mol. This level of precision is higher than the accuracy of most thermochemical measurements (typically 1-2 kcal/mol) and much higher than the accuracy of my calculated enthalpies.

On the other hand, while you can round off your final result, you should not round off the preliminary values. The rule-of-thumb is to always carry at least one digit past the one that you think will be uncertain. This means recording AM1 heats of formation to the closest 0.01 kcal/mol and recording ab initio total energies to the closest 0.00001 au (10^-5).